Preheat gas grill to medium-high heat (450-500 F).
Cut 2 large pieces of foil (10x15-inches approximately).
Wash and cut potatoes, pat dry with paper towel. Place in a bowl and add salt, pepper, oregano, garlic powder and oil. Toss to evenly coat potatoes in the seasoning.
Divide between both sheets. Wrap tightly.
Grill for 30-35 minutes. Check for doneness, if potatoes appear undercooked, cook for additional 5-10 minutes.
Remove from the grill and meat them cool for 5 minutes. Open the packets and drizzle lemon juice. Top with feta and parsley. Enjoy!